TALK=T;RUN(1,1) PHOTON USE AUTOPLOT file phi 5 cl msg LAMINAR PIPE FLOW WITH HEAT TRANSFER msg constant wall heat flux msg Reynolds number = 10 Prandtl number = 1.0 msg Velocity (W1) profile msg Blue line --- PHOENICS solution msg crosses --- analytical solution da 1 w1;da 1 w1a col3 1;blb4 2 msg pressto continue pause cl msg constant wall heat flux msg Reynolds number = 10 Prandtl number = 1.0 msg Temperature (H1) profile msg Blue line --- PHOENICS solution msg crosses --- analytical solution da 1 h1;da 1 h1a col3 1;blb4 2 msg press to continue pause msg press to end pause end END_USE DISPLAY DISPLAY The case considered is laminar flow and heat transfer of an incompressible, constant-property fluid in the hydrodynamically and thermally developed region of a of a circular tube. The heat transfer problem can be solved either with a constant wall heat flux ( QFCON=T ) or a constant wall temperature ( QFCON=F ). The Prandtl number is set to 1.0, but it should be noted that the Nusselt number is a function only of the thermal boundary condition, as follows: Nu = 3.656 for a constant surface temperature and Nu = 4.364 for a constant heat flux QIN. For the latter case, an analytical solution exists for the radial temperature profile: T = Tw-GAM*(0.1875+0.0625*(R/RO)**4-0.25*(R/RO)**2) where RO is the tube radius and GAM=4.*QIN/(K*R0) wherein K is the thermal conductivity of the fluid. ENDDIS ************************************************************ Group 1. Run Title and Number ************************************************************ ************************************************************ TEXT(1D Laminar Pipe Flow And Heat Trans ) ************************************************************ ************************************************************ IRUNN = 1 ;LIBREF = 14 ************************************************************ Group 2. Time dependence STEADY = T ************************************************************ Group 3. X-Direction Grid Spacing CARTES = F NX = 1 XULAST =1. XFRAC(1)=1. ************************************************************ Group 4. Y-Direction Grid Spacing NY = 30 YVLAST =0.1 YFRAC(1)=0.033333 ;YFRAC(2)=0.066667 YFRAC(3)=0.1 ;YFRAC(4)=0.133333 YFRAC(5)=0.166667 ;YFRAC(6)=0.2 YFRAC(7)=0.233333 ;YFRAC(8)=0.266667 YFRAC(9)=0.3 ;YFRAC(10)=0.333333 YFRAC(11)=0.366667 ;YFRAC(12)=0.4 YFRAC(13)=0.433333 ;YFRAC(14)=0.466667 YFRAC(15)=0.5 ;YFRAC(16)=0.533333 YFRAC(17)=0.566667 ;YFRAC(18)=0.6 YFRAC(19)=0.633333 ;YFRAC(20)=0.666667 YFRAC(21)=0.7 ;YFRAC(22)=0.733333 YFRAC(23)=0.766667 ;YFRAC(24)=0.8 YFRAC(25)=0.833333 ;YFRAC(26)=0.866667 YFRAC(27)=0.9 ;YFRAC(28)=0.933333 YFRAC(29)=0.966667 ;YFRAC(30)=1. ************************************************************ Group 5. Z-Direction Grid Spacing PARAB = F NZ = 1 ZWLAST =1. ZFRAC(1)=1. ************************************************************ Group 6. Body-Fitted Coordinates ************************************************************ Group 7. Variables: STOREd,SOLVEd,NAMEd ONEPHS = T NAME(7)=W1 ;NAME(14)=H1 NAME(149)=H1A ;NAME(150)=W1A * Y in SOLUTN argument list denotes: * 1-stored 2-solved 3-whole-field * 4-point-by-point 5-explicit 6-harmonic averaging SOLUTN(W1,Y,Y,N,N,N,Y) SOLUTN(H1,Y,Y,N,N,N,Y) SOLUTN(H1A,Y,N,N,N,N,Y) SOLUTN(W1A,Y,N,N,N,N,Y) ************************************************************ Group 8. Terms & Devices * Y in TERMS argument list denotes: * 1-built-in source 2-convection 3-diffusion 4-transient * 5-first phase variable 6-interphase transport TERMS(W1,N,N,Y,Y,Y,Y) TERMS(H1,N,N,Y,Y,Y,Y) DIFCUT =0.5 ;ZDIFAC =1. GALA = F ;ADDDIF = F USOURC = T ISOLX = -1 ;ISOLY = -1 ;ISOLZ = -1 ************************************************************ Group 9. Properties used if PRPS is not stored, and where PRPS = -1.0 if it is! RHO1 =1. ;TMP1 =0. ;EL1 =0. TSURR =0. ;TEMP0 =0. ;PRESS0 =0. DVO1DT =0. ;DRH1DP =0. EMISS =0. ;SCATT =0. RADIA =0. ;RADIB =0. ENUL =0.02 ;ENUT =0. PRNDTL(W1)=1. ;PRNDTL(H1)=1. PRT(W1)=1. ;PRT(H1)=1. CP1 =1. ;CP2 =1. ************************************************************ Group 10.Inter-Phase Transfer Processes ************************************************************ Group 11.Initial field variables (PHIs) FIINIT(W1)=1. ;FIINIT(H1)=8. FIINIT(H1A)=1.0E-10 ;FIINIT(W1A)=1.0E-10 PATCH(IN1 ,INIVAL, 1, 1, 1, 1, 1, 1, 1, 1) INIT(IN1 ,H1A ,0. ,1.388788E-03 ) INIT(IN1 ,W1A ,0. ,1.999444 ) PATCH(IN2 ,INIVAL, 1, 1, 2, 2, 1, 1, 1, 1) INIT(IN2 ,H1A ,0. ,0.012492 ) INIT(IN2 ,W1A ,0. ,1.995 ) PATCH(IN3 ,INIVAL, 1, 1, 3, 3, 1, 1, 1, 1) INIT(IN3 ,H1A ,0. ,0.034662 ) INIT(IN3 ,W1A ,0. ,1.986111 ) PATCH(IN4 ,INIVAL, 1, 1, 4, 4, 1, 1, 1, 1) INIT(IN4 ,H1A ,0. ,0.067824 ) INIT(IN4 ,W1A ,0. ,1.972778 ) PATCH(IN5 ,INIVAL, 1, 1, 5, 5, 1, 1, 1, 1) INIT(IN5 ,H1A ,0. ,0.111867 ) INIT(IN5 ,W1A ,0. ,1.955 ) PATCH(IN6 ,INIVAL, 1, 1, 6, 6, 1, 1, 1, 1) INIT(IN6 ,H1A ,0. ,0.166644 ) INIT(IN6 ,W1A ,0. ,1.932778 ) PATCH(IN7 ,INIVAL, 1, 1, 7, 7, 1, 1, 1, 1) INIT(IN7 ,H1A ,0. ,0.231967 ) INIT(IN7 ,W1A ,0. ,1.906111 ) PATCH(IN8 ,INIVAL, 1, 1, 8, 8, 1, 1, 1, 1) INIT(IN8 ,H1A ,0. ,0.307617 ) INIT(IN8 ,W1A ,0. ,1.875 ) PATCH(IN9 ,INIVAL, 1, 1, 9, 9, 1, 1, 1, 1) INIT(IN9 ,H1A ,0. ,0.393333 ) INIT(IN9 ,W1A ,0. ,1.839444 ) PATCH(IN10 ,INIVAL, 1, 1, 10, 10, 1, 1, 1, 1) INIT(IN10 ,H1A ,0. ,0.48882 ) INIT(IN10 ,W1A ,0. ,1.799444 ) PATCH(IN11 ,INIVAL, 1, 1, 11, 11, 1, 1, 1, 1) INIT(IN11 ,H1A ,0. ,0.593742 ) INIT(IN11 ,W1A ,0. ,1.755 ) PATCH(IN12 ,INIVAL, 1, 1, 12, 12, 1, 1, 1, 1) INIT(IN12 ,H1A ,0. ,0.707731 ) INIT(IN12 ,W1A ,0. ,1.706111 ) PATCH(IN13 ,INIVAL, 1, 1, 13, 13, 1, 1, 1, 1) INIT(IN13 ,H1A ,0. ,0.83038 ) INIT(IN13 ,W1A ,0. ,1.652778 ) PATCH(IN14 ,INIVAL, 1, 1, 14, 14, 1, 1, 1, 1) INIT(IN14 ,H1A ,0. ,0.961242 ) INIT(IN14 ,W1A ,0. ,1.595 ) PATCH(IN15 ,INIVAL, 1, 1, 15, 15, 1, 1, 1, 1) INIT(IN15 ,H1A ,0. ,1.099838 ) INIT(IN15 ,W1A ,0. ,1.532778 ) PATCH(IN16 ,INIVAL, 1, 1, 16, 16, 1, 1, 1, 1) INIT(IN16 ,H1A ,0. ,1.245648 ) INIT(IN16 ,W1A ,0. ,1.466111 ) PATCH(IN17 ,INIVAL, 1, 1, 17, 17, 1, 1, 1, 1) INIT(IN17 ,H1A ,0. ,1.398117 ) INIT(IN17 ,W1A ,0. ,1.395 ) PATCH(IN18 ,INIVAL, 1, 1, 18, 18, 1, 1, 1, 1) INIT(IN18 ,H1A ,0. ,1.556653 ) INIT(IN18 ,W1A ,0. ,1.319444 ) PATCH(IN19 ,INIVAL, 1, 1, 19, 19, 1, 1, 1, 1) INIT(IN19 ,H1A ,0. ,1.720625 ) INIT(IN19 ,W1A ,0. ,1.239444 ) PATCH(IN20 ,INIVAL, 1, 1, 20, 20, 1, 1, 1, 1) INIT(IN20 ,H1A ,0. ,1.889367 ) INIT(IN20 ,W1A ,0. ,1.155 ) PATCH(IN21 ,INIVAL, 1, 1, 21, 21, 1, 1, 1, 1) INIT(IN21 ,H1A ,0. ,2.062176 ) INIT(IN21 ,W1A ,0. ,1.066111 ) PATCH(IN22 ,INIVAL, 1, 1, 22, 22, 1, 1, 1, 1) INIT(IN22 ,H1A ,0. ,2.23831 ) INIT(IN22 ,W1A ,0. ,0.972778 ) PATCH(IN23 ,INIVAL, 1, 1, 23, 23, 1, 1, 1, 1) INIT(IN23 ,H1A ,0. ,2.416992 ) INIT(IN23 ,W1A ,0. ,0.875 ) PATCH(IN24 ,INIVAL, 1, 1, 24, 24, 1, 1, 1, 1) INIT(IN24 ,H1A ,0. ,2.597408 ) INIT(IN24 ,W1A ,0. ,0.772778 ) PATCH(IN25 ,INIVAL, 1, 1, 25, 25, 1, 1, 1, 1) INIT(IN25 ,H1A ,0. ,2.778704 ) INIT(IN25 ,W1A ,0. ,0.666111 ) PATCH(IN26 ,INIVAL, 1, 1, 26, 26, 1, 1, 1, 1) INIT(IN26 ,H1A ,0. ,2.959992 ) INIT(IN26 ,W1A ,0. ,0.555 ) PATCH(IN27 ,INIVAL, 1, 1, 27, 27, 1, 1, 1, 1) INIT(IN27 ,H1A ,0. ,3.140347 ) INIT(IN27 ,W1A ,0. ,0.439444 ) PATCH(IN28 ,INIVAL, 1, 1, 28, 28, 1, 1, 1, 1) INIT(IN28 ,H1A ,0. ,3.318805 ) INIT(IN28 ,W1A ,0. ,0.319445 ) PATCH(IN29 ,INIVAL, 1, 1, 29, 29, 1, 1, 1, 1) INIT(IN29 ,H1A ,0. ,3.494367 ) INIT(IN29 ,W1A ,0. ,0.195 ) PATCH(IN30 ,INIVAL, 1, 1, 30, 30, 1, 1, 1, 1) INIT(IN30 ,H1A ,0. ,3.665995 ) INIT(IN30 ,W1A ,0. ,0.066111 ) INIADD = F FSWEEP = 1 NAMFI =CHAM ************************************************************ Group 12. Patchwise adjustment of terms Patches for this group are printed with those for Group 13. Their names begin either with GP12 or & ************************************************************ Group 13. Boundary & Special Sources PATCH(WALL ,NWALL , 1, 1, 30, 30, 1, 1, 1, 1) COVAL(WALL ,W1 ,1. ,0. ) COVAL(WALL ,H1 , FIXFLU ,1. ) PATCH(FDFW1DP ,VOLUME, 1, 1, 1, 30, 1, 1, 1, 1) COVAL(FDFW1DP ,W1 ,5.0E-03 , GRND1 ) PATCH(FDFCHF ,PHASEM, 1, 1, 1, 30, 1, 1, 1, 1) COVAL(FDFCHF ,H1 ,19.999998 , GRND1 ) PATCH(TFIX ,CELL , 1, 1, 1, 1, 1, 1, 1, 1) COVAL(TFIX ,H1 ,1. ,0. ) XCYCLE = F EGWF = T WALLCO = GRND2 ************************************************************ Group 14. Downstream Pressure For PARAB ************************************************************ Group 15. Terminate Sweeps LSWEEP = 8 ;ISWC1 = 4 LITHYD = 2 ;LITFLX = 1 ;LITC = 5 ;ITHC1 = 1 SELREF = T RESFAC =1.0E-05 ************************************************************ Group 16. Terminate Iterations LITER(W1)=10 ;LITER(H1)=20 ENDIT(W1)=1.0E-03 ;ENDIT(H1)=1.0E-03 ************************************************************ Group 17. Relaxation RELAX(W1,FALSDT,0.027778) RELAX(H1,FALSDT,1.0E+09) RELAX(H1A,LINRLX,1.) RELAX(W1A,LINRLX,1.) OVRRLX =0. EXPERT = F ;NNORSL = F ************************************************************ Group 18. Limits VARMAX(W1)=1.0E+06 ;VARMIN(W1)=-1.0E+06 VARMAX(H1)=1.0E+10 ;VARMIN(H1)=-1.0E+10 VARMAX(H1A)=1.0E+10 ;VARMIN(H1A)=-1.0E+10 VARMAX(W1A)=1.0E+10 ;VARMIN(W1A)=-1.0E+10 ************************************************************ Group 19. Data transmitted to GROUND FDFSOL = T PARSOL = F ISG62 = 1 SPEDAT(SET,GXMONI,PLOTALL,L,T) ************************************************************ Group 20. Preliminary Printout ************************************************************ Group 21. Print-out of Variables INIFLD = F ;SUBWGR = F * Y in OUTPUT argument list denotes: * 1-field 2-correction-eq. monitor 3-selective dumping * 4-whole-field residual 5-spot-value table 6-residual table OUTPUT(W1,Y,N,Y,Y,Y,Y) OUTPUT(H1,Y,N,Y,Y,Y,Y) OUTPUT(H1A,Y,N,Y,N,N,N) OUTPUT(W1A,Y,N,Y,N,N,N) ************************************************************ Group 22. Monitor Print-Out IXMON = 1 ;IYMON = 30 ;IZMON = 1 NPRMON = 100000 ;NPRMNT = 1 ;TSTSWP = -1 UWATCH = T ;USTEER = T HIGHLO = F ************************************************************ Group 23.Field Print-Out & Plot Control NPRINT = 100000 ;NUMCLS = 5 NYPRIN = 1 ;IYPRF = 1 ;IYPRL = 10000 IPLTF = 1 ;IPLTL = -1 ;NPLT = 1 ISWPRF = 1 ;ISWPRL = 100000 ITABL = 3 ;IPROF = 1 ABSIZ =0.5 ;ORSIZ =0.4 NTZPRF = 1 ;NCOLPF = 50 ICHR = 2 ;NCOLCO = 45 ;NROWCO = 20 No PATCHes yet used for this Group ************************************************************ Group 24. Dumps For Restarts SAVE = T ;NOWIPE = F NSAVE =CHAM STOP